A tank initially contains 120 L of pure fresh water A mixtur

A tank initially contains 120 L of pure fresh water. A mixture containing a concentration of 4 g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. If S(t) is the amount of salt in the tank, then The initial value problem modeling the amount of salt in the tank is dS/dt = -1/60(S - 480), S(0) = 0. Find the expression for S(t) and determine the amount of salt in the tank as t rightarrow infinity.

Solution

dS/dt = -(S-480)/60

dS/(S-480) = - dt/60

ln(S-480)= -tc/60

S(t)= 480 + ke^-t/60

S(0) = 0. Implies k = -480.

So, S(t) = 480 - 480e^-t/60

as t tends to infinity amount of salt is 480g.